Introduction to Knot Theory
November 2nd, 2018
This site contains information on the lecture “Knots” given in autumn 2015 at Cardiff University, School of Mathematics.
News and Announcements
— none currently —
Organisational matters
Resources
Many resources on knot theory exist, from classical textbooks over lecture notes to picture galleries, videos and software. Here I list a few of them.
Books
- Colin Adams: The Knot Book (Freeman and Company, 2001)
An easy to read elementary introduction to knot theory. Gives good explanations of many of the relevant concepts, but does not cover all the material of this course. Still highly recommended as a first reading. - Charles Livingston: Knot Theory (Math. Ass. of America, 1993)
Another very good introduction to knot theory, more mathematical than the one by Adams. - Peter Cromwell (Cambridge University Press, 2004) Another good introduction to knot theory, more mathematical than the one by Livingston – often more technical than the style of this lecture will be.
- Louis Kauffman: Knots and Physics (World Scientific, 1991) A large but very readable book on theory. Most of the topics covered in this course can be found in Part I. We will not touch the material in Part II.
Lecture Notes
- A knot theory course at Warwick (2007), by Brian Sanderson from the University of Warwick.
- Knot Knotes (2015), by Justin Roberts from the University of San Diego.
Websites
- The Knot Atlas
A user-editable atlas of knots with many tables of knots, such as this one. - A Knot Zoo
Another table of knots and links. - Knots on the Web
An extensive list of web resources on many topics related to knots.
Videos
- Unraveling of a complicated looking knot into the unknot.
- Animation of a Brunnian link.
- A youtube channel with some introductory videos on knot theory, by Carlo H. Séquin from UC Berkeley.
Software
- KnotPlot A versatile programme for visualising knots and manipulating them, including some functions to compute mathematical invariants and several educational demonstrations. Has a free trial version. The website also hosts many pictures of knots in space — all pictures of knots displayed on this site are made with knotplot.
- A collection of knot theory demonstrations, interactive with the Wolfram CDF Player.
- The Mathematica Knot Theory Package. See also here.
Exercises and Lectures
This material is no longer available online, please refer to the links above instead.